I received my A.B and M.A. in Mathematics from the University of California, Berkeley in 1976 and 1978 respectively. In 1982 I earned my Ph.D. in Mathematics from the University of Utah under the supervision of Ronald J. Stern. After receiving my doctorate I was awarded a National Science Foundation Postdoctoral Fellowship which allowed me to visit the Courant Institute of Mathematical Sciences at New York University. Subsequently I held positions at Rutgers University, Oregon State University, and Pomona College before coming to Pitzer in 1989. I have spent time visiting the University of Melbourne, Australia, the University of Hawaii, Manoa, and the Mathematical Sciences Research Institute, Berkeley, California. I retired from Pitzer College in 2018.
My research interests are primarily in knot theory and low-dimensional topology. While working at Rutgers, I had the good fortune to hear Vaughan Jones speak about a "New Polynomial Invariant of Knots" at the Institute for Advanced Study in Princeton. Within a few months I was one of several people that found the 2-variable generalization of the Jones polynomial, now knows as the Homfly-PT polynomial. Following this, I wrote several papers with Jozef Przytycki about skein modules of 3-manifolds and worked on other problems that arise from the study of the skein polynomials of knots.
Over the years I have collaborated on the tabulation of all prime alternating knots through 18 crossings and prime nonalternating knots through 16 crossings. Together with Morwen Thistlethwaite, we have written a program called Knotscape that allows ready access to the knot tables as well as the computation of various knot invariants such as skein polynomials, representations of the fundamental group of a knot into permutation groups, and a number of hyperbolic invariants.
I am also interested in hyperbolic knots and various geometric knot invariants such as the A-polynomial. Most recently I have focussed on other invariants of knots, especially ones related to representations of the knot group, and also knot quandles.
Here is a list of my publications.
During the three summers of 2005, 2006, and 2007, I was director of the Claremont Colleges Mathematics REU and directed undergraduate students in summer research projects.
I supervised the following students' Senior Thesis in Mathematics while in Claremont.
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